An optical fiber conventionally includes an optical core, which transmits and/or amplifies an optical signal, and an optical cladding, which confines the optical signal within the core. Accordingly, the refractive index of the core nc is typically greater than the refractive index of the outer cladding ng (i.e., nc>ng).
The refractive index profile is generally classified according to the graphical appearance of the function that associates the refractive index with the radius of the optical fiber. Conventionally, the distance r to the center of the optical fiber is shown on the x-axis, and the difference between the refractive index (at radius r) and the refractive index of the optical fiber's outer cladding is shown on the y-axis. The refractive index profile is referred to as a “step” profile, a “trapezoidal” profile, an “alpha” profile, or a “triangular” profile for graphs having the respective shapes of a step, a trapezoid, an alpha, or a triangle. These curves are generally representative of the optical fiber's theoretical profile (i.e., the set profile). Constraints in the manufacture of the optical fiber, however, may result in a slightly different actual profile.
Generally speaking, two main categories of optical fibers exist: multimode fibers and single-mode fibers. In a multimode fiber, for a given wavelength, several optical modes are propagated simultaneously along the optical fiber, whereas in a single-mode fiber the higher order modes are strongly attenuated.
Multimode graded-index fibers with an “alpha” profile of the central core have been used for many years, and their characteristics have been described in particular in “Multimode Theory of Graded Core Fibers” by D. Gloge et al., Bell system Technical Journal 1973, pp. 1563-1578, and summarized in “Comprehensive Theory of Dispersion in Graded Index Optical Fibers” by G. Yabre, Journal of Lightwave Technology, February 2000, Vol. 18, No. 2, pp. 166-177. Each of the above-referenced articles is hereby incorporated by reference in its entirety.
A graded-index profile (i.e., an alpha-index profile) can be described by a relationship between the refractive index value n and the distance r from the center of the optical fiber according to the following equation:
  n  =            n      1        ⁢                  1        -                  2          ⁢                                    Δ              ⁡                              (                                  r                                      r                    1                                                  )                                      α                              
wherein,
α≧1, and α is a non-dimensional parameter that is indicative of the shape of the refractive index profile;
n1 is the maximum refractive index of the multimode optical fiber's core;
r1 is the radius of the multimode optical fiber's core; and
  Δ  =            (                        n          1          2                -                  n          0          2                    )              2      ⁢              n        1        2            
where n0 is the minimum index of the multimode core, which generally corresponds to the index of the outer optical cladding (most often made of silica).
Each mode, however, is propagated with its own propagation constant with which an effective refractive index neff can be associated, which is a function of the refractive index profile of the optical fiber and the wavelength.
FIG. 1 depicts the refractive index profile of a comparative α-profile optical fiber. The radius of the optical fiber is plotted on the lower x-axis, and the α-profile of the optical fiber's refractive index is plotted on the left-side y-axis. As depicted, a multimode α-profile optical fiber has a central core profile with a rotational symmetry such that along any radial direction of the optical fiber the value of the refractive index decreases continuously from the center of the optical fiber to the core's periphery. FIG. 1 also shows the modes that are propagated within the optical fiber. The right-side y-axis shows the relative effective refractive indices of the propagation modes (i.e., the difference between the mode's effective refractive index and the outer optical cladding's refractive index). A reference called the “azimuthal index” (plotted on the upper x-axis) corresponds to each mode. Typically, the modes collect together in groups of visible modes in a horizontal direction of the graph. For example, the optical fiber shown in FIG. 1 includes 18 mode groups.
The numerical aperture (NA) of an optical fiber is defined by the following equation:NA=√{square root over (neff,max2−neff,min2)}where neff,min and neff,max are respectively the minimum and maximum effective refractive indices of the modes within the signal, measured at the fiber output under OFL (overfilled launch) conditions (i.e., when the excitation of the signal at the fiber input is uniform over all the propagation modes).
A general approximation of the numerical aperture (ON), however, may be obtained with the following equation:ON=√{square root over (nmax2−nmin2)}where nmax and nmin are respectively the maximum and minimum refractive indices of the optical fiber's refractive index profile.
Typically, a depressed trench is added between the central core and the outer optical cladding to reduce the bending losses of a multimode graded-index optical fiber. The addition of such a depressed trench, however, results in the development of additional propagation modes known as leaky modes.
FIG. 2 further depicts the refractive index profile of the comparative optical fiber shown in FIG. 1, with the addition of a depressed trench between the central core and the outer optical cladding. Additional propagation modes are observed below the zero value of the relative effective refractive index (i.e., with respect to FIG. 1 and defined by the refractive index of the outer optical cladding). These additional propagation modes (i.e., leaky modes) are placed in five mode groups. The leaky modes have effective refractive indices that are lower than those of the guided modes. These leaky modes increase the numerical aperture of graded-index optical fibers having a depressed trench in comparison to the graded-index optical fibers without a depressed trench. A difference in numerical aperture can cause losses during connections within a system that employs both (i) depressed trench graded-index fibers and (ii) graded-index fibers without a depressed trench. Thus, the addition of a depressed trench to a graded-index profile gives rise to an undesirable increase in the numerical aperture. Therefore, it is desirable to limit the increase of the numerical aperture caused by the addition of a depressed trench.
U.S. Patent Application Publication No. 2008/0166094 and International Publication No. WO 2008/085851, each of which is hereby incorporated by reference in its entirety, disclose the use of a depressed trench for reducing the bending losses in a graded-index optical fiber. The publications, however, do not disclose how to limit the increase of the numerical aperture (i.e., relative to the numerical aperture of a graded-index fiber without a depressed trench). In other words, these publications fail to disclose how to avoid a large increase in the numerical aperture due to the addition of a depressed trench.
International Publication No. WO 2006/010798, which is hereby incorporated by reference in its entirety, describes an optical fiber including a graded-index central core and a depressed trench. The graded-index profile of the central core is extended beneath the refractive index of the outer optical cladding to the bottom of the depressed trench. In other words, there is no abrupt drop in the refractive index at the start of the depressed trench, but instead there is a gradual decrease until the bottom of the depressed trench is reached. The extension of the alpha-shaped central core beneath the refractive index of the outer optical cladding to the bottom of the depressed trench limits the reduction in the bending losses while further increasing the numerical aperture. Furthermore, International Publication No. WO 2006/010798 does not disclose how to limit the increase of the numerical aperture (i.e., relative to the numerical aperture of a graded-index fiber without a depressed trench).
Therefore, a need exists for a graded-index optical fiber having reduced bending losses without a significantly increased numerical aperture.